Are referees harsher to the away team?

One of the most frequently cited explanations for home advantage is referee bias: referees being influenced by their surroundings, such as a raucous home crowd, to favour the home team. During a match, a referee must make frequent split-second decisions; could it be that, despite their best efforts to remain impartial, they have a tendency towards appeasing (or avoiding abuse from) the home crowd?

As you might expect, referee bias in football has been the subject of numerous studies. In a well-known experiment, forty professional referees were asked to watch highlights of the Liverpool vs Leicester match at Anfield in the 1998/99 season. Half watched the game with sound, the other half without. The authors found that the group that watched the game with sound was less likely to call fouls against the home team than the group that watched it without sound. Other studies have taken more empirical approaches, appearing to find evidence for a home-team bias when referees award penalties or issue yellow and red cards (e.g. here, here and here).

Referee bias cannot simply be measured purely in terms of fouls conceded or bookings given; if the home team spends the majority of its games defending against superior opponents, we might expect them to give away more fouls and receive more yellow cards. So to detect referee bias we need to separate it from the stronger impact of team superiority.

In the last blog I introduced a simple way of estimating team superiority – how much better one team is than their opponent – called rolling points difference (RPD). To recap quickly: RPD measures the difference in the number of points the home team and the away team have accumulated over their last 38 games (roughly, over the last year). 

I’m now going to use RPD to separate the impact of home advantage from team superiority and see if we can find any evidence of bias in refereeing decisions. 

Do away teams receive more cards?

While yellow and red cards don’t normally affect the score directly, they can certainly sway a game. Players on a yellow card become more wary of making tackles, and a red card puts a team at a numerical disadvantage. If referees have a propensity to be harsher on the away team it will affect the outcome of the game and could explain home advantage.

I’m going to search for evidence of biased refereeing by comparing fouls committed and yellow/red cards issued. Why? Surely they are highly correlated: a team that commits more fouls will receive more yellow cards. The difference is that a referee has only a fraction of a second to blow the whistle and call a foul; there isn’t much time to be influenced by anything other than what he has seen. Taking disciplinary action is different: the referee has time to decide whether to show the offending player a card or let them off, and this is where they could be influenced – albeit unwittingly – by their surroundings.

In Figure 1 I plot the percentage of all the fouls in a game (as called by the referee) that are committed by the away team (red line), and the percentage of all the yellow and red cards issued by the referee that are received by the away team (blue line). Both are plotted as a function of rolling points difference, separating team superiority from home advantage. The gray region shows the 95% confidence region around the ‘fouls committed’ line (red). To make the plot, I use all EPL results since the 2000/01 season. 

Figure 1: the percentage of fouls committed (red line) and cards received (blue line) by the away team as a function of team superiority (rolling points difference). The grey region shows the 95% confidence region around the fouls committed line.

This figure seems to tell a clear story: away teams appear to be systematically more heavily punished by the referee than the home team.

How does the figure show this?

Let’s start in the middle, where RPD indicates that the teams are evenly matched. The home and away teams commit almost exactly the same number of fouls: around 50% each. However, on average the away team receives significantly more cards than the away team (57% of cards issued to 43%). Put another way, for every 3 yellow cards the home team receives, the away team receives four, even though they committed the same number of fouls.

The effect actually becomes bigger when one team is superior to the other. When the home team is much better than the away team (to the right of the figure), it receives just one card for every two that the away team receives. But when the away team is superior, cards tend to be split evenly. 

Unless the away team is systematically committing more serious fouls than the home team, then this looks like evidence of refereeing bias to me (whether it is conscious or ‘unconscious’ bias is a different matter).  These results agree with those in published in this analysis, which also show referee bias to the home side even when the teams are evenly matched (albeit using a different methodology and data).

So, referees don’t seem to give preferential treatment to the home team when calling fouls (awarding free kicks) but do seem to punish the away team more severely when issuing yellow and red cards. This suggests that, in the time that elapses between the foul being given and a card issued, the referee is – consciously or otherwise – influenced by external factors. 

As I said in my first post on home advantage, I think there is more to home advantage than officiating bias, but the data indicates that it is an important part of the puzzle.